Open Access
Translator Disclaimer
December 2008 Empirical null and false discovery rate inference for exponential families
Armin Schwartzman
Ann. Appl. Stat. 2(4): 1332-1359 (December 2008). DOI: 10.1214/08-AOAS184


In large scale multiple testing, the use of an empirical null distribution rather than the theoretical null distribution can be critical for correct inference. This paper proposes a “mode matching” method for fitting an empirical null when the theoretical null belongs to any exponential family. Based on the central matching method for z-scores, mode matching estimates the null density by fitting an appropriate exponential family to the histogram of the test statistics by Poisson regression in a region surrounding the mode. The empirical null estimate is then used to estimate local and tail false discovery rate (FDR) for inference. Delta-method covariance formulas and approximate asymptotic bias formulas are provided, as well as simulation studies of the effect of the tuning parameters of the procedure on the bias-variance trade-off. The standard FDR estimates are found to be biased down at the far tails. Correlation between test statistics is taken into account in the covariance estimates, providing a generalization of Efron’s “wing function” for exponential families. Applications with χ2 statistics are shown in a family-based genome-wide association study from the Framingham Heart Study and an anatomical brain imaging study of dyslexia in children.


Download Citation

Armin Schwartzman. "Empirical null and false discovery rate inference for exponential families." Ann. Appl. Stat. 2 (4) 1332 - 1359, December 2008.


Published: December 2008
First available in Project Euclid: 8 January 2009

zbMATH: 1158.62047
MathSciNet: MR2655662
Digital Object Identifier: 10.1214/08-AOAS184

Keywords: brain imaging , genome-wide association , mixture model , Multiple comparisons , multiple testing , Poisson regression

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.2 • No. 4 • December 2008
Back to Top